Dr Jess Harvey, of Much Wenlock and Cressage medical practice, said her team were desperate to immunise as many patients as possible. But she said the unpredictable manner in which the vaccines were being distributed made it near-impossible to plan for this.
Dr Harvey said the issues affected the supply of both the Pfizer and the AstraZeneca vaccines which had recently been licensed for use in the UK.
"There's not much of an orderly system to it," she said.
"We get a very short window to request the vaccine, and then we are told at very short notice what we will be getting.
"But if we are going to vaccinate 1,000 people, all elderly and vulnerable, we need time to manage this."
Dr Harvey said the team at her practice was working extremely hard, but said in many cases they were being asked to arrange staffing with just 24-48 hours' notice.
"This is quite frustrating, we are desperate to immunise as many people as we can, but we aren't being given the opportunity, it needs to be organised in a more orderly way," she said.
Dr Harvey said it appeared to be a national rather than a regional problem, with practices across the country expecting similar problems.
She said she had been told that the first doses of the new AstraZeneca vaccine would be arriving next week.
Her comments came after the Prime Minister admitted there would be some difficulties in getting supplies of the vaccines through.
Boris Johnson said almost 1.5 million people have now been vaccinated against the disease and the Government intends to give everyone in care homes a jab by the end of January.
Mr Johnson stressed the NHS was ready to administer vaccines as quickly as they could be supplied by manufacturers.
He said: “This is a national challenge on a scale like nothing we’ve seen before and it will require an unprecedented national effort,” he said.
“Of course, there will be difficulties, appointments will be changed but the Army is working hand in glove with the NHS and local councils to set up our vaccine network and using battle preparation techniques to help us keep up the pace.”
On Thursday Health Secretary Matt Hancock visited Bloomsbury Surgery in London to launch the AstraZeneca vaccine, only to find deliveries had been delayed.
Dr Ammara Hughes said Mr Hancock was “quite surprised actually to learn that we don’t know when all of our deliveries are coming, they’re very ad hoc”.
Mr Hancock later said there were no delays in the supply of the vaccine, it was simply that producing it took time.
“The capacity constraint is the supply of the approved vaccine,” he said, rather than the ability to administer it to patients.
“That does not mean there has been a delay and it is not a criticism at all of the manufacturers, they are working as fast as they can, it’s that making this stuff is hard.”